A highway truck transverse oscillation amplitude prediction method based on trajectory data

Abstract

The application belongs to the technical field of intelligent transportation systems, and discloses a highway truck transverse oscillation amplitude prediction method based on trajectory data. The application fuses high-frequency floating truck data, road design data and truck driving dynamics information, obtains trajectory data through data preprocessing and abnormal data elimination, extracts a vehicle transverse oscillation index from the trajectory data, selects multiple independent variables, judges the influence relationship of the independent variables on the vehicle transverse oscillation index based on a layered regression method, obtains significant influence variables, and finally constructs a prediction model of the significant influence variables and the transverse oscillation amplitude based on a Gaussian regression process, effectively solving the problem of insufficient modeling capability of the truck transverse deviation behavior in the existing method, and improving the scientificity and robustness of the prediction.

Description

Technical Field

[0001] This application belongs to the field of intelligent transportation systems technology, specifically relating to a method for predicting the lateral oscillation amplitude of highway trucks based on trajectory data. Background Technology

[0002] Current regulations determine lane width primarily based on static vehicle dimensions and theoretical safety clearances, lacking in-depth consideration of the dynamic characteristics of actual vehicle trajectories. Studies show that trucks exhibit significant lateral oscillations during high-speed driving—that is, their trajectories exhibit periodic deviations and fluctuations in the lane's lateral direction. This dynamic deviation not only reflects the driver's control over the vehicle but also directly impacts the actual required lane space. Due to the lack of quantitative prediction methods for the amplitude of these lateral oscillations, current designs often employ conservative width values, resulting in safety redundancy in some road sections and failing to achieve an optimal balance between safety and economy.

[0003] In recent years, with the development of intelligent transportation technology, driving behavior analysis based on vehicle trajectory big data has provided a new technical approach for lane width optimization. Existing research mainly focuses on the trajectory characteristics analysis of small vehicles, while systematic research on the lateral oscillation patterns of trucks, which have higher centers of mass and greater inertia, remains lacking. In particular, under the influence of factors such as road alignment changes and environmental disturbances, an effective quantitative evaluation system for the dynamic characteristics of truck lateral deviation has not yet been established. This makes lane width optimization based on dynamic trajectory data lack theoretical support and technical means.

[0004] Therefore, accurately capturing the lateral oscillation characteristics of trucks and constructing a scientific oscillation amplitude prediction model has become a key technical bottleneck for improving the economic efficiency of highway design. Currently, there is still a gap in theoretical research in this field, and there is an urgent need to establish a lateral oscillation prediction method based on the actual operating characteristics of trucks. Summary of the Invention

[0005] The purpose of this application is to address the problems of the prior art by providing a method for predicting the lateral oscillation amplitude of highway trucks based on trajectory data.

[0006] To address the technical problem, the technical solution of this application is: a method for predicting the lateral oscillation amplitude of highway trucks based on trajectory data, comprising the following steps:

[0007] Step 1: Use the vehicle-mounted GPS positioning device to obtain high-frequency floating truck data as the truck's original trajectory data, and combine it with the real-view map and road design data to import the original trajectory data into the real-view map and match it with the road alignment in the road design data.

[0008] Step 2: Preprocess the raw trajectory data and remove outliers using truck driving dynamics indicators to obtain the trajectory data. Extract the vehicle lateral oscillation index from the trajectory data; the vehicle lateral oscillation index represents the lateral oscillation amplitude. THERE ;

[0009] Step 3: Select road curvature, road turning, and vehicle speed as independent variables, and determine the impact of these independent variables on the lateral oscillation amplitude based on hierarchical regression. THERE The influence relationship was determined, and the significantly influential independent variables were obtained.

[0010] Step 4: Construct a predictive model that significantly affects the independent variable and the horizontal oscillation amplitude based on the Gaussian regression process, and obtain the predictive model that significantly affects the independent variable and the horizontal oscillation amplitude. THERE The relationship is used to predict the lateral oscillation amplitude of trucks on road sections.

[0011] Preferably, the high-frequency floating truck data in step 1 is the original trajectory data of the floating truck under natural driving conditions, which is desensitized; the acquisition frequency of the original trajectory data is 1Hz, and the original trajectory data includes the vehicle ID, time, longitude, latitude, instantaneous speed of the vehicle per second, and the clockwise angle between the vehicle's driving direction and due north under natural driving conditions.

[0012] Preferably, the preprocessing in step 2 includes coordinate transformation and time transformation. Coordinate transformation converts the original trajectory data in the GCJ-02 coordinate system into trajectory data in the WGS-84 coordinate system using a coordinate transformation formula. The coordinate transformation formula is:

[0013] ;

[0014] In the formula:

[0015] , These are the longitude and latitude coordinates in the WGS-84 coordinate system, respectively.

[0016] , These are the longitude and latitude coordinates from the original trajectory data, respectively.

[0017] and These are deviation functions calculated based on geographic location.

[0018] Preferably, the time conversion involves converting the timestamp sequence of the original trajectory data into Beijing time using a time conversion formula, which is:

[0019] ;

[0020] In the formula:

[0021] Beijing time;

[0022] This is the timestamp sequence of the original trajectory data.

[0023] Preferably, in step 2, the truck's driving dynamics indicators include vehicle jerkiness, vehicle steering angle, and speed deviation. These indicators are calculated using trajectory data and compared with preset thresholds to remove abnormal data. The formula for calculating the truck's driving dynamics indicators is as follows:

[0024] ;

[0025] ;

[0026] ;

[0027] ;

[0028] ;

[0029] ;

[0030] In the formula:

[0031] , vehicles n exist t Moment X、Y Latitude and longitude coordinates, in meters;

[0032] The direction angle is expressed in rad.

[0033] For the vehicle's steering angle, rad·s -1 ;

[0034] The vehicle speed is calculated based on the trajectory data, in m·s. -1 ;

[0035] Vehicle acceleration, measured in m / s² -2 ;

[0036] For velocity deviation, m·s -1 ;

[0037] Let m be the instantaneous speed of the vehicle per second. -1 ;

[0038] For vehicle jerkiness, m·s -3 .

[0039] Preferably, in step 2, the vehicle lateral oscillation index is the lateral oscillation amplitude. THERE The calculation formula is as follows:

[0040] ;

[0041] In the formula:

[0042] THERE Let m be the lateral oscillation amplitude of the vehicle;

[0043] The leftmost distance, in meters, represents the vehicle's deviation from the desired trajectory.

[0044] Let m be the rightmost distance (m) from which the vehicle deviates from the desired trajectory.

[0045] Preferably, in step 3, the independent variable is determined based on hierarchical regression to determine the amplitude of the horizontal oscillation. The specific influencing factors are: road curvature, road turning, and vehicle speed are selected as independent variables, and the lateral oscillation amplitude is... Using the independent variable as the dependent variable, a hierarchical regression equation is constructed. Based on the hierarchical regression equation, the collinearity relationship of each independent variable is obtained. Furthermore, the F-test is used to obtain the effect of each independent variable on the horizontal oscillation amplitude. The magnitude of the influence is determined by the formula for calculating the hierarchical regression equation:

[0046] ;

[0047]

[0048] In the formula:

[0049] The coefficient of determination after regression of the dependent variable with other independent variables;

[0050] When the value is less than 10, there is no collinearity among the independent variables;

[0051] Y The dependent variable;

[0052] As the independent variable;

[0053] The coefficients of the hierarchical regression equation;

[0054] This represents the random error term in the hierarchical regression equation;

[0055] The independent variables that were significantly affected were road curvature and vehicle speed.

[0056] Preferably, step 4 specifically includes:

[0057] Step 4-1: Based on hierarchical regression, determine road curvature and vehicle speed as independent variables for the truck lateral oscillation amplitude prediction model;

[0058] Step 4-2: Prepare training samples; use the trajectory data obtained by removing outliers in Step 2 as the data for subsequent Gaussian regression, and extract a total sample size of [missing data]. n training dataset ( i =1, 2, ..., n ),in v i and Q i These are the first two numbers in the training dataset. i The vehicle's speed and the road curvature are the two input variables. , S i For the training dataset, the first i The lateral oscillation amplitude of each vehicle is the output value, which is used to calculate the prediction result of the lateral oscillation amplitude of the truck vehicle.

[0059] Step 4-3: Define the Gaussian regression process; In the Gaussian regression model, the output results include the mean function and the covariance function. First, define the mean function. Sum of covariance functions ,in These are the input samples from the training dataset. In addition to the training dataset For data samples other than those in the original text, the output value will be... Gaussian regression process This can be expressed as the following formula:

[0060] ;

[0061] Step 4-4: Gaussian Model Training; Before training the Gaussian model, the mean function... When set to 0, the exponential square kernel function is used as the covariance function, which is expressed as:

[0062] ;

[0063] In the formula:

[0064] These are kernel function parameters;

[0065] They are respectively noise variance and n An identity matrix of order 1;

[0066] Constructing the covariance matrix K , K elements in K ij For the training dataset, the first i Input variables and the j Input variables The covariance between them is expressed by the following formula:

[0067] ;

[0068] The kernel function parameters are determined using maximum likelihood estimation. and noise variance set The hyperparameters of the kernel function are denoted as Based on Bayesian theory and joint normal distribution theory, the training dataset The likelihood function is expressed as:

[0069] ;

[0070] In the formula:

[0071] S For all output values A set;

[0072] V, Q Input variables v and Q A set;

[0073] M Mean function A set;

[0074] for K The determinant of;

[0075] Transform the above likelihood function into a log-likelihood function. L ( ), which is expressed as:

[0076] ;

[0077] Taking the partial derivative, we get:

[0078] ;

[0079] In the formula:

[0080] To calculate the trace of the matrix;

[0081] for The i One element;

[0082] Adjusting hyperparameters using gradient ascent method To maximize the log-likelihood function L ( Then, the parameters are iteratively updated until convergence, resulting in the optimal kernel function parameters;

[0083] Steps 4-5: Prediction results and uncertainty estimation; for new input variables First, calculate the covariance matrix. , elements in yes and The covariance between them, i.e.:

[0084] ;

[0085] Then calculate Its own covariance :

[0086] ;

[0087] Finally, calculate the mean of the prediction results. and variance used to describe the uncertainty of the prediction results. The formula is:

[0088] ;

[0089] Step 4-6: Obtain the prediction model for the lateral oscillation amplitude of the truck based on steps 4-1 to 4-5.

[0090] Compared with the prior art, the advantages of this application are:

[0091] (1) This application proposes a method for predicting the lateral oscillation amplitude of highway trucks based on trajectory data. It integrates high-frequency floating truck data, road design data and truck driving dynamics information. Trajectory data is obtained through data preprocessing and outlier removal. The vehicle lateral oscillation index is extracted from the trajectory data. Multiple independent variables are selected and the influence relationship between the independent variables and the vehicle lateral oscillation index is determined based on hierarchical regression. Significantly influential independent variables are obtained. Finally, a prediction model of the significantly influential independent variables and the lateral oscillation amplitude is constructed based on Gaussian regression. This effectively solves the problem of insufficient modeling ability of truck lateral deviation behavior in existing methods and improves the scientificity and robustness of the prediction.

[0092] (2) This application proposes a truck driving dynamics index removal mechanism with vehicle jerkiness, vehicle steering angle and speed deviation as the core for abnormal data such as interweaving, fluctuation and adjacent lane interference in truck trajectory data. This significantly improves the purity of the dataset and provides a high-quality sample basis for modeling the lateral oscillation amplitude of trucks.

[0093] (3) In this application, road curvature, road turning and vehicle speed are selected as independent variables. Hierarchical regression is used to obtain the significantly influential independent variables. Based on the Gaussian regression process, the significantly influential independent variables and the lateral oscillation amplitude are constructed. THERE Compared to traditional linear methods, this predictive model is better able to reveal the complex nonlinear relationships between variables and provides uncertainty estimation results, ensuring the reliability and adaptability of the prediction.

[0094] (4) This application realizes the complete process from trajectory data processing to model construction, covering key links such as data acquisition, coordinate transformation, dynamic elimination, feature selection, model training and evaluation prediction. It can be widely applied to the prediction of lateral oscillation of trucks under different road conditions, providing a quantifiable basis for the dynamic optimization of lane width in highway design, filling the technical gap of the current specifications which are mainly based on static standards, and has significant engineering promotion value. Attached Figure Description

[0095] Figure 1 This is a flowchart illustrating a method for predicting the lateral oscillation amplitude of highway trucks based on trajectory data, as described in this application.

[0096] Figure 2 This is a schematic diagram of the vehicle lateral vibration index in Embodiment 1 of this application;

[0097] Figure 3 This is a schematic diagram of the road segment from which the original trajectory data was collected in Embodiment 1 of this application;

[0098] Figure 4 This is the style for matching trajectory data with a real-world map in Embodiment 2 of this application;

[0099] Figure 5 This refers to the upper boundary of the 90% confidence interval in the Gaussian regression process in Example 2 of this application;

[0100] Figure 6 The results are from the prediction model of the lateral oscillation amplitude of the truck in Embodiment 2 of this application. Detailed Implementation

[0101] The present application is described in detail below with reference to the accompanying drawings and specific embodiments, but the present application is not limited to these embodiments. The present application covers any alternatives, modifications, equivalent methods, and solutions made within the spirit and scope of the present application. To provide the public with a thorough understanding of the present application, specific details are described in detail in the following embodiments, but those skilled in the art will fully understand the present application even without these detailed descriptions.

[0102] like Figure 1 As shown, this application discloses a method for predicting the lateral oscillation amplitude of highway trucks based on trajectory data, including the following steps:

[0103] Step 1: Use the vehicle-mounted GPS positioning device to obtain high-frequency floating truck data as the truck's original trajectory data, and combine it with the real-view map and road design data to import the original trajectory data into the real-view map and match it with the road alignment in the road design data.

[0104] Step 2: Preprocess the raw trajectory data and remove outliers using truck driving dynamics indicators to obtain the trajectory data. Extract the vehicle lateral oscillation index from the trajectory data; the vehicle lateral oscillation index represents the lateral oscillation amplitude. THERE ;

[0105] Step 3: Select road curvature, road turning, and vehicle speed as independent variables, and determine the impact of these independent variables on the lateral oscillation amplitude based on hierarchical regression. THERE The influence relationship was determined, and the independent variables with significant influence were obtained; road curvature and road steering were obtained from road design data, and vehicle operating speed was obtained from trajectory data.

[0106] Step 4: Construct a predictive model that significantly affects the independent variable and the horizontal oscillation amplitude based on the Gaussian regression process, and obtain the predictive model that significantly affects the independent variable and the horizontal oscillation amplitude. THERE The relationship is used to predict the lateral oscillation amplitude of trucks on road sections.

[0107] Preferably, after obtaining the original trajectory data, it can be preprocessed first, and then the trajectory data can be imported into the real-world map and matched with the road alignment in the road design data.

[0108] Preferably, the high-frequency floating truck data in step 1 is the original trajectory data of the floating truck under natural driving conditions, with the environment being mainly daytime, dry road surface, and free-flowing traffic; the acquisition frequency of the original trajectory data is 1Hz, and the original trajectory data includes the desensitized vehicle ID (Imei), time (Location Time), longitude (Lat), latitude (Lon), instantaneous speed of the vehicle per second (Speed), and the clockwise angle between the vehicle's driving direction and due north (Bearing) under natural driving conditions.

[0109] Preferably, the preprocessing in step 2 includes coordinate transformation and time transformation. Coordinate transformation converts the original trajectory data in the GCJ-02 coordinate system into trajectory data in the WGS-84 coordinate system using a coordinate transformation formula to ensure the confidentiality and security of the geographic data. The coordinate transformation formula is:

[0110] ;

[0111] In the formula:

[0112] , These are the longitude and latitude coordinates in the WGS-84 coordinate system, respectively.

[0113] , These are the longitude and latitude coordinates from the original trajectory data, respectively.

[0114] and These are deviation functions calculated based on geographic location.

[0115] Preferably, the time conversion involves converting the timestamp sequence of the original trajectory data into Beijing time using a time conversion formula, which is:

[0116] ;

[0117] In the formula:

[0118] Beijing time;

[0119] This is the timestamp sequence of the original trajectory data.

[0120] Preferably, in step 2, the truck's driving dynamics indicators include vehicle jerkiness, vehicle steering angle, and speed deviation. These indicators are calculated using trajectory data and compared with preset thresholds to remove abnormal data. The formula for calculating the truck's driving dynamics indicators is as follows:

[0121] ;

[0122] ;

[0123] ;

[0124] ;

[0125] ;

[0126] ;

[0127] In the formula:

[0128] , vehicles n exist t Moment X、Y Latitude and longitude coordinates, in meters;

[0129] The direction angle is expressed in rad.

[0130] For the vehicle's steering angle, rad·s -1 ;

[0131] The vehicle speed is calculated based on the trajectory data, in m·s. -1 ;

[0132] Vehicle acceleration, measured in m / s² -2 ;

[0133] For velocity deviation, m·s -1 ;

[0134] Let m be the instantaneous speed of the vehicle per second. -1 ;

[0135] For vehicle jerkiness, m·s -3 .

[0136] Preferably, in step 2, the vehicle lateral oscillation index is the lateral oscillation amplitude. THERE The calculation formula is as follows:

[0137] ;

[0138] In the formula:

[0139] THERE Let m be the lateral oscillation amplitude of the vehicle;

[0140] The leftmost distance, in meters, represents the vehicle's deviation from the desired trajectory.

[0141] Let m be the rightmost distance (m) from which the vehicle deviates from the desired trajectory.

[0142] Preferably, in step 3, the independent variable is determined based on hierarchical regression to determine the amplitude of the horizontal oscillation. The specific influencing factors are: road curvature, road turning, and vehicle speed are selected as independent variables, and the lateral oscillation amplitude is... Using the independent variable as the dependent variable, a hierarchical regression equation is constructed. Based on the hierarchical regression equation, the collinearity relationship of each independent variable is obtained. Furthermore, the F-test is used to obtain the effect of each independent variable on the horizontal oscillation amplitude. The magnitude of the influence is determined by the formula for calculating the hierarchical regression equation:

[0143] ;

[0144]

[0145] In the formula:

[0146] The coefficient of determination after regression of the dependent variable with other independent variables;

[0147] When the value is less than 10, there is no collinearity among the independent variables;

[0148] Y The dependent variable;

[0149] As the independent variable;

[0150] The coefficients of the hierarchical regression equation;

[0151] This represents the random error term in the hierarchical regression equation;

[0152] The independent variables that were significantly affected were road curvature and vehicle speed.

[0153] Preferably, step 4 specifically includes:

[0154] Step 4-1: Based on hierarchical regression, determine road curvature and vehicle speed as independent variables for the truck lateral oscillation amplitude prediction model;

[0155] Step 4-2: Prepare training samples; use the trajectory data obtained by removing outliers in Step 2 as the data for subsequent Gaussian regression, and extract a total sample size of [missing data]. n training dataset ( i =1, 2, ..., n ),in v i and Q i These are the first two numbers in the training dataset. i The vehicle's speed and the road curvature are the two input variables. , S i For the training dataset, the first iThe lateral oscillation amplitude of each vehicle is the output value, which is used to calculate the prediction result of the lateral oscillation amplitude of the truck vehicle.

[0156] Step 4-3: Define the Gaussian regression process; In the Gaussian regression model, the output results include the mean function and the covariance function. First, define the mean function. Sum of covariance functions ,in These are the input samples from the training dataset. In addition to the training dataset For data samples other than those in the original text, the output value will be... Gaussian regression process This can be expressed as the following formula:

[0157] ;

[0158] Step 4-4: Gaussian Model Training; Before training the Gaussian model, the mean function... When set to 0, the exponential square kernel function is used as the covariance function, which is expressed as:

[0159] ;

[0160] In the formula:

[0161] These are kernel function parameters;

[0162] They are respectively noise variance and n An identity matrix of order 1;

[0163] Constructing the covariance matrix K , K elements in K ij For the training dataset, the first i Input variables and the j Input variables The covariance between them is expressed by the following formula:

[0164] ;

[0165] The kernel function parameters are determined using maximum likelihood estimation. and noise variance set The hyperparameters of the kernel function are denoted as Based on Bayesian theory and joint normal distribution theory, the training dataset The likelihood function is expressed as:

[0166] ;

[0167] In the formula:

[0168] S For all output values A set;

[0169] V, Q Input variables v and Q A set;

[0170] M Mean function A set;

[0171] for K The determinant of;

[0172] Transform the above likelihood function into a log-likelihood function. L ( ), which is expressed as:

[0173] ;

[0174] Taking the partial derivative, we get:

[0175] ;

[0176] In the formula:

[0177] To calculate the trace of the matrix;

[0178] for The i One element;

[0179] Adjusting hyperparameters using gradient ascent method To maximize the log-likelihood function L ( Then, the parameters are iteratively updated until convergence, resulting in the optimal kernel function parameters;

[0180] Steps 4-5: Prediction results and uncertainty estimation; for new input variables First, calculate the covariance matrix. , elements in yes and The covariance between them, i.e.:

[0181] ;

[0182] Then calculate Its own covariance :

[0183] ;

[0184] Finally, calculate the mean of the prediction results. and variance used to describe the uncertainty of the prediction results. The formula is:

[0185] ;

[0186] Step 4-6: Obtain the prediction model for the lateral oscillation amplitude of the truck based on steps 4-1 to 4-5.

[0187] Example 1

[0188] This embodiment proposes a method for predicting the lateral oscillation amplitude of highway trucks based on trajectory data. The method includes the following steps:

[0189] Step 1: Use the vehicle-mounted GPS positioning device to obtain high-frequency floating truck data as the truck's original trajectory data, and combine it with the real-view map and road design data to import the original trajectory data into the real-view map and match it with the road alignment in the road design data.

[0190] During implementation, the first step is to acquire high-frequency floating truck data to record vehicle position and speed information. GPS positioning devices are installed on the trucks and are used for data collection, including information such as truck number, time, coordinates, direction, and speed. The onboard GPS positioning devices boast high data acquisition accuracy, accurately capturing vehicle location information; they offer extremely wide coverage; and their large spatiotemporal dimensions allow for complete recording of long-term, cross-regional truck travel trajectories. With a collection frequency set to 1Hz, they enable real-time and accurate recording of truck travel status on highways.

[0191] like Figure 3 As shown, the original trajectory data of the trucks was provided by the "One Road, Three Parties" platform of a highway management company. The data was collected from three highways in a certain region of China, all with a design speed of 120 km / h. -1 The data collected consisted of two-way four-lane highways, encompassing various road alignment combinations. Data collection spanned from June to September 2023, primarily conducted in free-flow traffic environments and covering diverse weather conditions and different time periods, including day and night. This provided a rich and diverse dataset for studying the actual movement trajectories of trucks.

[0192] By combining road design data, road station numbers are extracted to match the original trajectory data with the road station numbers.

[0193] Step 2: Preprocessing the raw trajectory data mainly includes coordinate transformation and time transformation:

[0194] The coordinate transformation converts the original trajectory data in the GCJ-02 coordinate system into trajectory data in the WGS-84 coordinate system using a coordinate transformation formula to ensure the confidentiality and security of the geographic data. The formula is as follows:

[0195] ;

[0196] In the formula:

[0197] X and Y These are the latitude and longitude coordinates in the WGS-84 coordinate system.

[0198] , These are the longitude and latitude coordinates from the original trajectory data, respectively.

[0199] and These are deviation functions calculated based on geographic location, and these two functions are usually calculated using empirical formulas and constant parameters.

[0200] The time conversion involves converting the timestamp sequence of the original trajectory data into Beijing time using a time conversion formula, which is:

[0201] ;

[0202] In the formula:

[0203] Beijing time;

[0204] This is the timestamp sequence of the original trajectory data.

[0205] Abnormal data such as weaving, deviation, fluctuation, and adjacent lane interference are removed from the trajectory data using truck driving dynamics indicators, and the lateral oscillation characteristics of the vehicle are extracted.

[0206] For vehicle trajectory samples exhibiting data anomalies and data drift, the trajectory data is cleaned based on the rationality of its kinematic parameters. Data anomalies and data drift refer to short-term, drastic fluctuations caused by factors such as severe weather, resulting in a mismatch between the coordinate or velocity information in the trajectory data and the actual vehicle's motion parameters. Therefore, vehicle jerkiness, vehicle steering angle, and speed deviation are selected as indicators to judge the accuracy of the trajectory data.

[0207] From a spatial perspective, the lateral oscillation amplitude and lateral oscillation period are two core indicators that can effectively characterize the spatial characteristics of vehicle lateral oscillations. From a temporal perspective, the lateral oscillation frequency indicator is introduced to measure the activity level of vehicle lateral oscillation behavior over time.

[0208] like Figure 2 The figure shows a schematic diagram of the vehicle lateral oscillation index. The truck's driving trajectory is constructed within the XY coordinate axis. The black dashed line in the figure is the desired trajectory line, and the red solid line is the actual driving trajectory.

[0209] The formula for calculating the vehicle lateral vibration index is as follows:

[0210] ;

[0211] ;

[0212] ;

[0213] In the formula:

[0214] THERE The lateral vibration amplitude of the vehicle is expressed in meters (m).

[0215] D The lateral oscillation period of the vehicle is expressed in meters (m).

[0216] T The lateral oscillation frequency of the vehicle is expressed in seconds (s).

[0217] The leftmost distance, in meters, represents the vehicle's deviation from the desired trajectory.

[0218] Let m be the rightmost distance (m) from which the vehicle deviates from the desired trajectory.

[0219] Experiments have verified that the horizontal oscillation amplitude... THERE It can effectively characterize vehicle vibration, and based on this, the lateral vibration amplitude is selected. THERE As an indicator of lateral vehicle vibration.

[0220] Step 3: Select road curvature, road turning, and vehicle speed as independent variables, and determine the impact of these independent variables on the lateral oscillation amplitude based on hierarchical regression. THERE The influence relationship was determined, and the independent variables with significant influence were obtained; road curvature and road steering were obtained from road design data, and vehicle operating speed was obtained from trajectory data.

[0221] We extracted road alignment data from 50 road segments, along with truck speed and lateral oscillation data from these segments. We designed three factors—road curvature, road turning, and vehicle speed—as independent variables, and the 95th percentile of lateral oscillation amplitude as the dependent variable. The independent variables with significant influence were found to be road curvature and vehicle speed.

[0222] Step 4: Construct a predictive model based on the Gaussian regression process that significantly affects the independent variable and the amplitude of lateral oscillations, and obtain the road curvature. Vehicle speed Lateral sway amplitude of truck Based on the relationship, we can further predict the lateral oscillation amplitude of trucks on the road section.

[0223] First, based on the hierarchical regression results, road curvature and vehicle speed are determined as independent variables in the truck lateral oscillation amplitude prediction model. A Gaussian regression process is then used to construct the model, which involves four steps: preparing training samples, defining the Gaussian process, training the Gaussian model, and estimating the prediction results and uncertainties. Finally, the relationship between truck lateral oscillation amplitude and road curvature and vehicle speed is obtained, thus enabling the prediction of truck lateral oscillation amplitude.

[0224] The prediction model for the lateral oscillation amplitude of the truck is shown below:

[0225] ;

[0226] In the formula:

[0227] This represents the 95th percentile value of the lateral oscillation amplitude of the truck.

[0228] For road curvature;

[0229] The vehicle's operating speed.

[0230] Example 2

[0231] In this embodiment, the method for predicting the lateral oscillation amplitude of a truck specifically includes the following steps:

[0232] Step 1: Use the vehicle-mounted GPS positioning device to obtain high-frequency floating truck data as the truck's raw trajectory data;

[0233] Step 2: Perform coordinate and time transformations on the raw high-frequency floating truck data. The coordinates obtained from the collected raw trajectory data are latitude and longitude coordinates in the "GCJ-02" coordinate system. Using the Python programming language, the raw GCJ-02 coordinate system (Mars coordinate system) data is processed to achieve the transformation to the projected coordinate system, thus providing a suitable data foundation for subsequent research on the lateral oscillation of trucks. The collected raw trajectory data includes... The value represents a timestamp, measured in milliseconds, indicating the total number of seconds since January 1, 1970, 00:00:00 UTC (Coordinated Universal Time). It needs to be converted to Beijing time (UTC+8) to match the time information in the trajectory data and facilitate subsequent research. After completing the conversion of the original trajectory data's spatiotemporal information, the velocity unit is first changed from milliseconds... -1 Convert to km·h -1 The trajectory data was numbered according to information such as the device number, with each number representing a truck. Then, the trajectory data was imported into the real-world map and matched with the road alignment, combining the real-world map with road design data. The preprocessed trajectory data is shown in Table 1.

[0234] Table 1. Style of preprocessed trajectory data

[0235]

[0236] like Figure 4 As shown, this is a partial example of matching trajectory data with a real-world map. The red dots represent truck trajectory data, and the white labels represent road marker information indicating the vehicle's location. By comparing the road design data, it was found that the GPS data used in the study can match the actual road alignment well, with high matching accuracy.

[0237] After preprocessing the raw trajectory data, it is necessary to clean the GPS trajectory anomaly data. Anomalies refer to data that, during the collection process, are easily affected by factors such as weather, structures, and equipment, inevitably resulting in some data with spatiotemporal anomalies. Anomalies mainly include four types of problems: missing data, duplicate data, data anomalies, and data drift. This application, based on truck driving dynamics indicators, considers the rationality of kinematic parameters and the continuity of the time series to determine whether the relevant indicators of the trajectory data are within a reasonable range. Trajectory data outside the reasonable range are marked as anomalies and removed, and the lateral oscillation amplitude is also considered. THERE Horizontal oscillation cycle D Horizontal oscillation frequency T A dataset of vehicle lateral oscillation indicators was constructed, as shown in Table 2:

[0238] Table 2 Vehicle Lateral Oscillation Indicator Dataset

[0239]

[0240] The horizontal oscillation amplitude THERE It can effectively characterize vehicle vibration, and based on this, the lateral vibration amplitude is selected. THERE As an indicator of lateral vehicle vibration.

[0241] Step 3: Use hierarchical regression to determine the impact of road curvature, road steering, and vehicle speed on the lateral oscillation amplitude. THERE The influence relationship was investigated. To ensure the stability and accuracy of the regression model, road alignment data for 50 road segments, along with data on truck speeds and lateral oscillation amplitudes on these segments, were extracted. Road curvature, road steering, and vehicle speed were designed as independent variables, with the 95th percentile of lateral oscillation amplitude as the dependent variable. This was primarily because lane width needs to be reasonable enough to ensure safe operation for most vehicles; therefore, the 95th percentile of lateral oscillation amplitude for all vehicles within the road segment was used as the dependent variable. Statistical analysis of truck speed data within the road segments revealed a range of 75–95 km / h. -1 The speed range contained 93.12% of the effective trajectory data points. To prevent inaccurate model results and overfitting caused by uneven data distribution, the study selected a speed distribution of 75–95 km / h. -1 Trucks were used as the research object, and the data was collected at a speed of 5 km / h. -1 To differentiate truck trajectory data by step size, the trajectory data of trucks within a certain speed range are considered as a sample. The 95th percentile of the lateral oscillation amplitude of trucks within this whole is calculated as the dependent variable. At the same time, at least 50 trajectory data points are ensured for each interval to guarantee the reliability of the results. Some data structure examples are shown in Table 3:

[0242] Table 3 Data Structure Examples

[0243]

[0244] This embodiment of hierarchical regression analysis involves three models: road curvature, vehicle speed, and road steering. Independent variables are added to the models sequentially, with each addition representing a new stratum. The three strata are stratum 1, stratum 2, and stratum 3. To avoid collinearity issues among the independent variables, VIF (Variable Interest Scale) is first used to diagnose collinearity. The collinearity diagnosis results for road curvature, vehicle speed, and road steering using VIF data are shown in Table 4. It can be found that the VIF values ​​are all less than 10, proving that there is no collinearity problem among the independent variables, and the relationships between the independent variables are good.

[0245] Table 4. Results of the Multicollinearity Test (VIF)

[0246]

[0247] After diagnosis, based on the idea of ​​hierarchical regression, the influence of different road curvatures, vehicle speeds, and road steering on the 95th percentile of the lateral oscillation amplitude of trucks was systematically evaluated. The hierarchical regression results for the 95th percentile of the lateral oscillation amplitude are shown in Table 5.

[0248] Table 5 Results of Stratified Regression Analysis of Lateral Oscillation Amplitude

[0249]

[0250] From the table, we can find that:

[0251] (1) Model 1 only includes the road curvature radius as the independent variable. The value of 0.653 indicates that the road curvature radius has a high explanatory power for the 95th percentile of the lateral oscillation amplitude of trucks, and that road curvature can explain 65.3% of the variation in the 95th percentile of lateral oscillation amplitude. This suggests that road curvature is a key factor affecting the lateral oscillation amplitude of trucks. The F-test of the model (F=220.189, p<0.05) is significant, and the regression coefficient is 0.009, indicating a positive correlation between curvature and the 95th percentile of lateral oscillation amplitude.

[0252] (2) After introducing vehicle speed as an independent variable based on Model 1, Model 2 showed a significant change in the F value (p<0.05), indicating that the addition of vehicle speed as an indicator has explanatory significance for the change in the lateral oscillation amplitude of trucks. The value increased from 0.653 to 0.753, which means that vehicle speed has 10% explanatory significance for the 95th percentile of lateral oscillation amplitude. The regression coefficient is 0.006, which proves that there is a positive correlation between vehicle speed and the 95th percentile of lateral oscillation amplitude.

[0253] (3) Model 3 further incorporates road turning as a third independent variable based on Model 2. However, the change in the F value is not significant. Specifically, the result is: ΔF = 0.928, p > 0.05. The value changed by 0.001, close to 0. This indicates that, in the context of the current study, the inclusion of road steering does not substantially contribute to explaining the change in the 95th percentile of the lateral oscillation amplitude of trucks.

[0254] Therefore, the independent variables that have a significant impact are road curvature and vehicle speed.

[0255] Step 4: Randomly select 70% of the data samples from the trajectory data as the training set, and use the remaining 30% as the test set for validation. It is necessary to ensure that the ratio of daytime to nighttime trajectory data in the training and validation sets is maintained at approximately 1:1, and to measure the lateral oscillation amplitude of the truck. With vehicle speed and road curvature The model is trained using the vehicle speeds in the test set. and road curvature The input is fed into the trained Gaussian regression model to calculate the corresponding prediction results.

[0256] like Figure 5 As shown, to ensure that the design specifications for highway lane widths fully meet the safety and comfort needs of the vast majority of drivers, the output value at the upper boundary of the 90% confidence interval is used as the predicted result for lateral oscillation amplitude. This means that, statistically, the lateral deviation of vehicles will be less than this predicted value with a probability exceeding 95%. This design method has a higher safety redundancy than the traditional mean method, effectively covering extreme lateral oscillation amplitudes caused by differences in driving behavior, and avoiding the waste of land resources caused by over-design.

[0257] like Figure 6 The image shows the prediction model results for the lateral oscillation amplitude of a truck, combined with the vehicle's operating speed. (Speed) and road curvature (Curvature) and the lateral oscillation amplitude of the truck The relationship model will include the operating speed of some vehicles. With road curvature After inputting the relevant parameters into the model, the predicted values ​​of the lateral oscillation amplitude are shown in Table 6. The predicted values ​​show that as the vehicle speed and the radius of curvature of the road increase, the lateral oscillation amplitude of the truck will further increase.

[0258] Table 6 Comparison of Predicted and Actual Values

[0259]

[0260] To better understand vehicle speed and road curvature Lateral oscillation amplitude of trucks To mitigate the impact of the Gaussian process model, this application employs three indicators—root mean square error, mean absolute error, and mean absolute percentage error—to quantify the accuracy of the Gaussian process model.

[0261] Table 6 shows the different vehicle operating speeds Sections and different road curvatures Lateral sway of the unloading truck The mean value of the lateral oscillation amplitude and some results of the mean value of the lateral oscillation amplitude predicted by Gaussian process regression were used to calculate the root mean square error (RMSE) of the lateral oscillation amplitude prediction model as 3.954%, the mean absolute error (MAE) as 0.034, and the mean absolute percentage error (MAPE) as 5.696%. These results indicate that the lateral oscillation amplitude prediction model constructed using Gaussian process regression can effectively describe the relationship between the upper boundary of the 90% confidence interval of the lateral oscillation amplitude of trucks and the relationship between truck speed and road curvature radius. The model has high accuracy, and the lane width determined by the model structure meets the accuracy requirements.

[0262] Based on the aforementioned accuracy assessment, the truck lateral vibration amplitude prediction model proposed in this application provides a quantitative, data-driven scientific basis for highway lane width design. This helps traffic design and management departments achieve rational allocation and optimization of road resources while ensuring traffic safety, thereby improving the operational efficiency and economy of highways. Future research can further introduce more influencing factors, such as crosswinds, lane edge conditions, and traffic density, to expand the model's applicability and improve the prediction accuracy of vehicle lateral behavior under complex conditions. This method provides theoretical and technical support for the refined design of highways oriented towards actual operational characteristics, promotes the intelligent and refined development of traffic engineering design, and provides important decision support and reference value for the optimization and implementation of intelligent transportation systems.

[0263] The preferred embodiments of this application have been described in detail above. However, this application is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of this application.

[0264] Many other changes and modifications can be made without departing from the concept and scope of this application. It should be understood that this application is not limited to the specific embodiments, and the scope of this application is defined by the appended claims.

Claims

1. A method for predicting the lateral oscillation amplitude of highway trucks based on trajectory data, characterized in that, Includes the following steps: Step 1: Use the vehicle-mounted GPS positioning device to obtain high-frequency floating truck data as the truck's original trajectory data, and combine it with the real-view map and road design data to import the original trajectory data into the real-view map and match it with the road alignment in the road design data. Step 2: Preprocess the raw trajectory data and remove outliers using truck driving dynamics indicators to obtain the trajectory data. Extract the vehicle lateral oscillation index from the trajectory data; the vehicle lateral oscillation index represents the lateral oscillation amplitude. LA ; Step 3: Select road curvature, road turning, and vehicle speed as independent variables, and determine the impact of these independent variables on the lateral oscillation amplitude based on hierarchical regression. LA The influence relationship was determined, and the significantly influential independent variables were obtained. The method based on hierarchical regression is used to determine the effect of independent variables on the horizontal oscillation amplitude. The specific influencing factors are: road curvature, road turning, and vehicle speed are selected as independent variables, and the lateral oscillation amplitude is... Using the independent variable as the dependent variable, a hierarchical regression equation is constructed. Based on the hierarchical regression equation, the collinearity relationship of each independent variable is obtained. Furthermore, the F-test is used to obtain the effect of each independent variable on the horizontal oscillation amplitude. The magnitude of the influence is determined by the formula for calculating the hierarchical regression equation: ； ； In the formula: The coefficient of determination after regression of the dependent variable with other independent variables; When the value is less than 10, there is no collinearity among the independent variables; Y The dependent variable; As the independent variable; The coefficients of the hierarchical regression equation; This represents the random error term in the hierarchical regression equation; The independent variables that had a significant impact were road curvature and vehicle speed. Step 4: Construct significant independent variables and horizontal oscillation amplitude based on Gaussian regression process LA The predictive model yielded significant influences on the independent variables and the amplitude of horizontal oscillations. LA The relationship is used to predict the lateral oscillation amplitude of trucks on road sections.

2. The method for predicting the lateral oscillation amplitude of highway trucks based on trajectory data according to claim 1, characterized in that, In step 1, the high-frequency floating truck data is the original trajectory data of the floating truck under natural driving conditions, which is desensitized. The acquisition frequency of the original trajectory data is 1Hz. The original trajectory data includes the vehicle ID, time, longitude, latitude, instantaneous speed of the vehicle per second, and the clockwise angle between the vehicle's driving direction and due north under natural driving conditions.

3. The method for predicting the lateral oscillation amplitude of highway trucks based on trajectory data according to claim 2, characterized in that, Step 2, the preprocessing, includes coordinate transformation and time transformation. Coordinate transformation converts the original trajectory data in the GCJ-02 coordinate system into trajectory data in the WGS-84 coordinate system using a coordinate transformation formula. The coordinate transformation formula is as follows: ； In the formula: , These are the longitude and latitude coordinates in the WGS-84 coordinate system, respectively. , These are the longitude and latitude coordinates from the original trajectory data, respectively. and These are deviation functions calculated based on geographic location.

4. The method for predicting the lateral oscillation amplitude of highway trucks based on trajectory data according to claim 3, characterized in that, The time conversion involves converting the timestamp sequence of the original trajectory data into Beijing time using a time conversion formula, which is: ； In the formula: Beijing time; This is the timestamp sequence of the original trajectory data.

5. The method for predicting the lateral oscillation amplitude of highway trucks based on trajectory data according to claim 4, characterized in that, In step 2, the truck's driving dynamics indicators include vehicle jerkiness, vehicle steering angle, and speed deviation. These indicators are calculated using trajectory data and compared with preset thresholds to remove abnormal data. The formula for calculating the truck's driving dynamics indicators is as follows: ； ； ； ； ； ； In the formula: , vehicles n exist t Moment X, Y Latitude and longitude coordinates, in meters; The direction angle is expressed in rad. For the vehicle's steering angle, rad·s -1 ; The vehicle speed is calculated based on the trajectory data, in m·s. -1 ; Vehicle acceleration, measured in m / s² -2 ; For velocity deviation, m·s -1 ; Let m be the instantaneous speed of the vehicle per second. -1 ; For vehicle jerkiness, m·s -3 .

6. The method for predicting the lateral oscillation amplitude of highway trucks based on trajectory data according to claim 5, characterized in that, In step 2, the vehicle lateral oscillation indicator is the lateral oscillation amplitude. LA The calculation formula is as follows: ； In the formula: LA Let m be the lateral oscillation amplitude of the vehicle; The leftmost distance, in meters, represents the vehicle's deviation from the desired trajectory. Let m be the rightmost distance (m) from which the vehicle deviates from the desired trajectory.

7. The method for predicting the lateral oscillation amplitude of highway trucks based on trajectory data according to claim 6, characterized in that, Step 4 specifically includes: Step 4-1: Based on hierarchical regression, determine road curvature and vehicle speed as independent variables for the truck lateral oscillation amplitude prediction model; Step 4-2: Prepare training samples; use the trajectory data obtained by removing outliers in Step 2 as the data for subsequent Gaussian regression, and extract a total sample size of [missing data]. n training dataset ( i =1, 2, ..., n ),in v i and Q i These are the first two numbers in the training dataset. i The vehicle's speed and the road curvature are the two input variables. , S i For the training dataset, the first i The lateral oscillation amplitude of each vehicle is the output value, which is used to calculate the prediction result of the lateral oscillation amplitude of the truck vehicle. Step 4-3: Define the Gaussian regression process; In the Gaussian regression model, the output results include the mean function and the covariance function. First, define the mean function. Sum of covariance functions ,in These are the input samples from the training dataset. In addition to the training dataset For data samples other than those in the original text, the output value will be... Gaussian regression process This can be expressed as the following formula: ； Step 4-4: Gaussian Model Training; Before training the Gaussian model, the mean function... When set to 0, the exponential square kernel function is used as the covariance function, which is expressed as: ； In the formula: These are kernel function parameters; They are respectively noise variance and n An identity matrix of order 1; Constructing the covariance matrix K , K elements in K ij For the training dataset, the first i Input variables and the j Input variables The covariance between them is expressed by the following formula: ； The kernel function parameters are determined using maximum likelihood estimation. and noise variance set The hyperparameters of the kernel function are denoted as Based on Bayesian theory and joint normal distribution theory, the training dataset The likelihood function is expressed as: ； In the formula: S For all output values A set; V, Q Input variables v and Q A set; M Mean function A set; for K The determinant; Transform the above likelihood function into a log-likelihood function. L ( ), which is expressed as: ； Taking the partial derivative, we get: ； In the formula: To calculate the trace of the matrix; for The i One element; Adjusting hyperparameters using gradient ascent method To maximize the log-likelihood function L ( Then, the parameters are iteratively updated until convergence, resulting in the optimal kernel function parameters; Steps 4-5: Prediction results and uncertainty estimation; for new input variables First, calculate the covariance matrix. , elements in yes and The covariance between them, i.e.: ； Then calculate Its own covariance : ； Finally, calculate the mean of the prediction results. and variance used to describe the uncertainty of the prediction results. The formula is: ； Step 4-6: Obtain the prediction model for the lateral oscillation amplitude of the truck based on steps 4-1 to 4-5.

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